Question

已知点p(0,0)和圆x^2+y^2-4x-6y-12=0,过P做直线交圆C与AB两点,则AB长为整数的有几条

Answer 1

x^2+y^2-4x-6y-12=0

(x-2)^2+(y-3)^2=25

AB最长=直径=2*5=10

AB最短时

圆心到P距离=√13

∴此时AB=2*√(25-13)=4√3≈6.9

∴6.9AB=7,8,9,10

AB长为整数的有4条